a boulder is thrown launched into the air with an upward velocity of 184 ft per second. Its height h in feet after t seconds is given by the function h(t)=-16t^2 +184t+6. How long does it take the boulder to reach its maximum height? What is the boulder maximum height?
a- 11.6 ft 5.75 seconds
b- 549 ft 11.5 seconds
c- 549 ft 5.75 seconds
d- 23.2 ft 11.6 seconds
We just did this.
h(t)=8(23-2t^1)t + 6
so at t=0, and t=11.5, h(t)=6, so max occures half way at t=11.5/2 seconds...
hmax=-16(11.5/2)^2+184(11.5/2)+6
looks like b is the closest...
thank you
To find the maximum height of the boulder and the time it takes to reach that height, we need to find the vertex of the function h(t)=-16t^2+184t+6.
The vertex of a quadratic function in the form h(t) = at^2 + bt + c is given by the formula: t = -b / (2a).
In our case, a = -16 and b = 184. So, plugging these values into the formula, we get: t = -184 / (2 * -16) = 11.5 seconds.
Therefore, the correct answer is option b.
Now, to find the maximum height, we substitute this value of t into the function h(t) = -16t^2 + 184t + 6 to get: h(11.5) = -16(11.5)^2 + 184(11.5) + 6 = 549 ft.
Therefore, the boulder reaches a maximum height of 549 ft.
So, the correct answer is option b: 549 ft, 11.5 seconds.